A mixer is a device that is designed to receive two frequency signals and combines the signals to generate mixing products at frequencies that are the sum and difference of the received frequencies. In many cases, only one of the mixing products is desired. The other product is referred to as the “image.” Image reject mixers are devices that ideally produce only the sum or difference product, but not both. The implementation of an image reject mixer involves two discrete mixers. The phase of the signals applied to the two mixers is controlled such that, when the two mixer outputs are combined, the desired products of the mixers add constructively and the image products add destructively. In the ideal case, the image is completely cancelled leaving only the desired product.
For image reject mixers, two factors contribute to the degree of image rejection. The first factor is the gain balance between the two discrete mixers within the device. Specifically, if one of the two discrete mixers generates products of greater magnitude than the other mixer, the image products of the two mixers will not completely cancel each other. The second factor is the phase relationship associated with the mixing. Specifically, if there is a phase error in the quadrature phase relationship between the signals driving the mixers, the image output products of the two mixers will not be exactly 180 degrees out of phase and hence will not completely cancel each other.
To achieve a relatively high degree of image rejection, the gain of the discrete mixers and the quadrature angle relationships in an image reject mixer can be calibrated. Typically, an iterative approach is applied in which the gain and the phase relationship are repetitively adjusted and the magnitude of the image is measured. Eventually, operating values defining the gain and phase relationship can be located that substantially null the image product. Additionally, a number of mathematical techniques can be employed to cause the operating values to converge more quickly. These techniques are generally related to “Newton's Method” of root finding in which the derivative of the image product magnitude versus the gain and phase are used to find the null.